The characterization of tissue viscoelastic properties requires the measurement of tissue motion over a region of interest at frequencies that significantly exceed the frame rates of conventional ultrasound systems. In this paper, we propose that the bandpass sampling technique be applied to tissue motion sampling. With this approach, high-frequency signals limited to a frequency band can be sampled and reconstructed without aliasing at a sampling frequency that is lower than the Nyquist rate. We first review this approach and discuss the selection of the tissue excitation frequency band and of the feasible sampling frequencies that allow signal reconstruction without aliasing. We then demonstrate the approach using simulations based on the finite element method and ultrasound simulations. Finally, we perform experiments on tissue-mimicking materials and demonstrate accurate motion estimation using a lower sampling rate than that required by the conventional sampling theorem. The estimated displacements were used to measure the elasticity and viscosity in a phantom in which an inclusion has been correctly delineated. Thus, with bandpass sampling, it is feasible to use conventional beamforming on diagnostic ultrasound systems to perform high-frequency dynamic elastography. The method is simple to implement because it does not require beam interleaving, additional hardware, or synchronization.